How do you do this problem?

x^3 - 2x^2 - 3x + 12
____________________

x + 2

Use synthetic Division to solve more easily.

You can search online for a website that explains synthetic division.

5x^2-17x+3 over x-4

To do this problem, you need to perform polynomial long division. Here's how you can approach it:

Step 1: Write the dividend and divisor in standard form.
The dividend: x^3 - 2x^2 - 3x + 12
The divisor: x + 2

Step 2: Start dividing.
First, check the highest degree terms. Divide x^3 by x, which gives you x^2. Write x^2 above the line.

x^2
---------------
x + 2 | x^3 - 2x^2 - 3x + 12

Step 3: Multiply the divisor (x + 2) by the current quotient (x^2) and write the result below the dividend.

x^2
--------------
x + 2 | x^3 - 2x^2 - 3x + 12
x^3 + 2x^2
--------------
- 5x + 12

Step 4: Subtract the product from the dividend.

x^2
--------------
x + 2 | x^3 - 2x^2 - 3x + 12
x^3 + 2x^2
--------------
- 5x + 12
- 5x - 10
--------------
22

Step 5: Repeat the process with the new dividend. Now the remainder is 22.

Continue dividing until the remainder does not have a higher degree term than the divisor or it becomes zero. In this case, since we have a remainder of 22, the final quotient will be x^2 - 5x + 22 and the remainder will be 22.

Therefore, the expression x^3 - 2x^2 - 3x + 12 divided by x + 2 is equal to x^2 - 5x + 22 with a remainder of 22.